help to understand how residual standard deviation can differ at different points on X I read in more than one place that residual standard deviation can differ at different points on X. I cannot understand this statement. 
I find this while learning the very basics, so for me the standard deviation of the residuals is a single unique number, and I see no way how this single number can change depending on the xi being a simple number calculated across all samples. 
I guess I must be missing some necessary intermediate concept/steps.
I would be very grateful is someone can explain this to me in a very basic way

My question was not clear trying to improve it: what is not clear to me is if there is such a thing as the standard-deviation of a specific point/sample, ie. if we have x <- 1:5, y <- c(10,6,12,15,2) and y ~ x, is there a formal concept of standard deviation of residual of a single sample and a formula to calculate it ? ie. can I, and if yes how do I calculate the standard deviation of the residual corresponding to x=1,y=10 ? of that corresponding to x=2,y = 6? ...
 A: EDIT : 
My answer was indeed wrong (thank you @Glen_b). I cannot delete it as it has been validated.
All I can do is to redirect you to this answer written by Alecos Papadopoulos.
In short, if you have a simple model:
$y_i = \beta_0 + \beta_1*x_i + u_i$
then your $ith$ residual will be like $\hat{u_i} = y_i - \hat{y_i} = (\beta_0 - \hat{\beta_0}) + (\beta_1 - \hat{\beta_1})*x_i + u_i$.
If $Var(u_i) = \sigma$ then $Var(\hat{u_i}) = \sigma(1-\frac{1}{n} - \frac{(x_i - \bar{x})^2}{\sum(x_i^2-\bar{x}^2)})$.
All the calculation are explained in the link, and I could not do any better.
A: I may have found a sort of answer. 
In some cases (analysis of residuals, this terminology might be unprecise) standard deviation is calculated excluding a sample/data-point. 
The standard deviation so calculated, though calculated over all samples (minus one, "that" sample/data-point), is uniquely "identified" by the sample/data-point due to its exclusion from the computation.
(A similar thing seems to happen for standard error calculated for similar purposes)
